Surface bound states in a bounded XXZ-model

Hans Gerd Evertz, Martin Ganahl, Elias Rabel

S. Brandt, Hans Dieter Dahmen

Masanori Kohno

Dynamical properties of frustrated XXZ models in the Ising limit on spatially anisotropic two-dimensional lattices are investigated by a weak-coupling approach from the one-dimensional limit. Restricting the Hilbert space to that spanned by exact eigenstates of XXZ chains in the Ising limit, we calculate dynamical structure factor 5 -+ (k,ω) in spatially anisotropic two-dimensional systems. As in the case of frustrated Heisenberg models [M.Kohno, et al. , Nat. Phys. 3, 790 (2007)], spinons form bound states through hopping process between chains. We calculate the density-density correlation function of spinons in the Ising limit, and show that spinons in the bound state hop together as a pair, although those in a continuous spectrum behave almost independently. We discuss possible implications of the present results on fractionalization of bosonic and fermionic particles in spatially anisotropic frustrated systems with strong repulsion.

S. Brandt, Hans Dieter Dahmen

Sébastien Dusuel, Michael Kamfor, Kai Phillip Schmidt +2 more

We analyze the properties of low-energy bound states in the transverse-field Ising model and in the XXZ model on the square lattice. To this end, we develop an optimized implementation of perturbative continuous unitary transformations. The Ising model is studied in the small-field limit which is found to be a special case of the toric code model in a magnetic field. To analyze the XXZ model, we perform a perturbative expansion about the Ising limit in order to discuss the fate of the elementary magnon excitations when approaching the Heisenberg point.

Christopher D. Parmee, Nigel R. Cooper

Chains of coupled two-level atoms behave as one-dimensional quantum spin systems, exhibiting free magnons and magnon bound states. While these excitations are well studied for closed systems, little consideration has been given to how they are altered by the presence of an environment. This will be especially important in systems that exhibit nonlocal dissipation, e.g., systems in which the magnons decay due to optical emission. In this paper, we consider free magnon excitations and two-magnon bound states in an XXZ chain with nonlocal dissipation. We prove that while the energy of the bound state can lie outside the two-magnon continuum of energies, the decay rate of the bound state has to always lie within the two-magnon continuum of decay rates. We then derive analytically the bound-state solutions for a system where both the XY interaction and nonlocal dissipation are nearest neighbor or next-nearest neighbor, finding that the inclusion of nonlocal dissipation allows more freedom in engineering the energy and decay rate dispersions for the bound states. Finally, we numerically study a model of an experimental setup that should allow the realization of dissipative bound states by using Rydberg-dressed atoms coupled to a photonic crystal waveguide. We demonstrate that this model can exhibit many key features of our simpler models.